Please Help. I have a midterm, and this is an example question of what might be on it.

The manager of a CD store has found that if the price of CD is p(x)=80-x/6, then x CDs will be sold. Find an expression for the total revenue from the sale of x CDs (hint: revenue= demand x price). Use your expression to determine the maximum revenue.

Oct 21st 2007, 08:55 PM

coe236

Revenue is price*demand, so the price(x) here is 80-x/6 and the demand is x, so the expression would be x*(80-x/6)= 80x - x^2/6. Max revenue, in terms of microeconomics, is usually at equilibrium or the midpoint on the demand curve. If thats given, then you just plug it into the expression

Oct 21st 2007, 08:55 PM

Jhevon

Quote:

Originally Posted by aphan19

Please Help. I have a midterm, and this is an example question of what might be on it.

The manager of a CD store has found that if the price of CD is p(x)=80-x/6, then x CDs will be sold. Find an expression for the total revenue from the sale of x CDs (hint: revenue= demand x price). Use your expression to determine the maximum revenue.

is the formula: ? if so, you should use parentheses to indicate that.

Revenue = demand * Price, that is, it is the number of items sold times the price each item is sold for.

thus the revenue function is given by:

this is a parabola, it's maximum occurs at its vertex

the vertex of a parabola, is the point

the answer to your last question is the y-coordinate of that formula

can you find it?

(you could also complete the square to get the vertex, which method do you prefer?)

Oct 21st 2007, 09:05 PM

aphan19

It is not (80-x)/6, it is actually 80-(x/6). Sorry, for not adding the parenthesis in my problem before. If the problem is actually 80-(x/6), now what do I do to solve it?

Oct 21st 2007, 09:15 PM

Jhevon

Quote:

Originally Posted by aphan19

It is not (80-x)/6, it is actually 80-(x/6). Sorry, for not adding the parenthesis in my problem before. If the problem is actually 80-(x/6), now what do I do to solve it?

do exactly what we said before: multiply through by x, and solve for the vertex of the resulting parabola by whatever method you feel comfortable with